The binary puzzle uses only two symbols, and three rules govern everything. Each row and column must hold an equal number of each. Never three alike in a row, horizontally or vertically. And no two rows may be identical, nor any two columns. The same puzzle turns up under many names: Takuzu, Binairo and 0h h1 are the most common, and LinkedIn's daily Tango runs the same three rules with suns and moons instead of discs.
How to solve it
Two alike side by side force the opposite at both ends, because a third in a row is forbidden. That is the most common opening and it nearly always gives you somewhere to start.
Two alike with a gap between them work the same way in reverse: the gap must take the opposite symbol, or three would line up. Sweep for both patterns before reaching for anything cleverer.
Count. As soon as half a row is filled with one symbol, the rest of that row is determined. This is the rule people forget, and it settles the endgame of almost every puzzle.
The unique-rows rule is rarely needed, but decisive when it is. If one row is complete and another is two cells from finished, the second cannot become a copy of the first.
What makes a puzzle hard
Grid size and how many cells are given at the start. Six by six falls almost entirely to the two patterns above. Ten by ten demands active counting and occasionally leaning on the rule that no two rows may match.
A worked example
A row in an eight-grid has four of one symbol placed and four cells empty. Since every row must hold four of each, all remaining cells take the other symbol, wherever they happen to sit. Counting resolves the whole row at once, without looking at a single pattern.
The most common mistake
Hunting only for triples and forgetting to count. People get stuck with a board that breaks no obvious rule but where one row already holds too many of a symbol. Check the tallies regularly, not just the patterns.